In [1]} several model structures on
\({K}/B\)  are introduced. The model structure on \({K}/B\)  that we will be interested in
has its origins in the work [2]} of Schwänzl and Vogt. In [2]}
(see also [4]} and [1]})
the authors consider a topological bicomplete category \({C}\)  and
define three classes of morphisms: \(h\) -equivalences, \(h\) -fibrations and
\(\bar{h}\) -cofibrations. A morphism \(f\colon X\rightarrow Y\)  in \({C}\)  is an
\(h\) -equivalence if and only if it is a homotopy equivalence, defined in
terms of the cylinder objects \(X\otimes I\)  and \(Y\otimes I\)  where
\(I\)  denotes the unit interval. A morphism \(f\colon X\rightarrow Y\)  is called an
\(h\) -fibration if and only if it has the LLP (left lifting property) with respect to all
morphisms of the form \(Z\otimes \lbrace 0\rbrace \rightarrow Z\otimes I\) , while \(f\)  is
called an \(\bar{h}\) -cofibration if and only if
\(X\otimes I\cup _{X\otimes 0} Y\otimes 0 \rightarrow Y\otimes I\)  has the
LLP with respect to all \(h\) -fibrations in \({C}\) .
